Internal problem ID [2911]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 6
Problem number: 163.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_rational, _Riccati]
Solve \begin {gather*} \boxed {y^{\prime } x +x^{2}+y^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(x*diff(y(x),x)+x^2+y(x)^2 = 0,y(x), singsol=all)
\[ y \relax (x ) = -\frac {c_{1} x \BesselY \left (1, x\right )}{c_{1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )}-\frac {\BesselJ \left (1, x\right ) x}{c_{1} \BesselY \left (0, x\right )+\BesselJ \left (0, x\right )} \]
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 45
DSolve[x y'[x]+x^2+y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x (Y_1(x)+c_1 J_1(x))}{Y_0(x)+c_1 J_0(x)} \\ y(x)\to -\frac {x J_1(x)}{J_0(x)} \\ \end{align*}